Question

You receive the Dean’s Scholarship which pays you RMB 100,000 annually for 3 years. The first payment will be made one year from today. What is the Present Value of these 3 payments if interest rate is 3% p.a.? A. RMB 246,168 B. RMB 257,710 C. RMB 267,301 D. RMB 282,861 E. RMB 288,388

A bank manager tells you the monthly rate is 0.5%. What is the Effective Annual Rate? A. 2.43% B. 3.66% C. 6.17% D. 12.68% E. 79.58%

The Annual Percentage Rate is 12%. What is the semi-annually rate? A. 1% B. 2% C. 3% D. 4% E. 6%

The nominal interest rate is 8% p.a. and the inflation rate is 6% p.a. Determine the real interest rate using the exact method. A. 1.02% p.a. B. 1.69% p.a. C. 1.89% p.a. D. 1.98% p.a. E. 2.56% p.a

What is the price of a 5.0% annual coupon bond with a $1,000 face value which matures in 5 years? The yield-to-maturity (YTM) is 3.0% p.a. A. $ 913.42 B. $ 945.54 C. $1,000.00 D. $1,056.57 E. $1,091.59

You are paying $ 1,516.15 for a 3.0% annual coupon bond with a $1,000 face value, which matures in 30 years? Determine the yield-to-maturity (YTM). A. 1.0% B. 2.0% C. 3.0% D. 4.0% E. 5.0%

There is a 3-year bond which pays 4% annual coupons. You use a $1,000 face value and a required return rate of 2.15% p.a. in your calculations. Determine the Current Yield. A. 2.93% B. 3.80% C. 4.62% D. 5.40% E. The correct answer cannot be determined because the bond price is not provided.

What is the price of a 5.0% semi-annual coupon bond with a $1,000 face value which matures in 5 years? The yield-to-maturity (YTM) is 3.0% p.a. A. $1,070.68 B. $1,092.22 C. $1,113.76 D. $1,230.55 E. $1,255.55

Answer 1

1. Present value of the payments= discount all the future cashflows with a rate of 3%

Present value=(100000/(1+3%))+(100000/(1+3%)^2)+(100000/(1+3%)^3)=$282,861.1

Option D is correct

2.The formula for effective annual interest rate=((1+r)^n)-1

r=monthly rate=0.5%

n=number periods=12 (12 months in a year)

effective annual rate=((1+0.5%)^12)-1=6.17%

Option C is correct

3. The semi-annual rate=annual rate/2=12%/2=6%

Option E is correct

4. The real interest rate=((1+nominal rate)/(1+inflation rate))-1

=((1+8%)/(1+6%))-1

=1.89%

Option C is correct

5. The market price of the bond needs to find using PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

rate=yield to maturity=3%

nper=maturity period=5

pmt=coupon payment=(5%*1000)=50

fv=1000

=PV(3%,5,50,1000,0)

PV=$1091.59

Option E is correct

6. The YTM can be found using RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

nper=30

pmt=(3%*1000)=30

pv=1516.15

fv=1000

=RATE(30,30,-1516.15,1000,0)

RATE=1%

Option A is correct

7.First find the price of the bond

=PV(rate,nper,pmt,fv,type)

rate=2.15%

nper=maturity period=3

pmt=coupon payment=(4%*1000)=40

fv=1000

=PV(2.15%,3,40,1000,0)

PV=$1053.20

Current yield=annual coupon/Price of the bond=40/1053.20=3.80%

Option B is correct

8. =PV(rate,nper,pmt,fv,type)

Here the payments are semi-annual

rate=yield to maturity=3%/2=1.5%

nper=maturity period=5*2=10

pmt=semi-annual coupon payment=(5%*1000)/2=25

fv=1000

=PV(1.5%,10,25,1000,0)

PV=$1092.22

Option B is correct